What is the answer to x/(2-i)+y/(3-i)=2 ?

The answer to x/(2-i)+y/(3-i)=2 is x=-10,y=20

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x/(2-i)+y/(3-i)=2

\frac{x}{2 - i} + \frac{y}{3 - i} = 2

x = - 10, y = 20

Solution steps

\frac{x}{2 - i} + \frac{y}{3 - i} = 2

Find Least Common Multiplier of

2 - i, 3 - i : (2 - i) (3 - i)

Multiply by LCM=

(2 - i) (3 - i)

\frac{x}{2 - i} (2 - i) (3 - i) + \frac{y}{3 - i} (2 - i) (3 - i) = 2 (2 - i) (3 - i)

Expand

(3 x + 2 y) + i (- x - y) = 10 - 10 i

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[3 x + 2 y = 10 - x - y = - 10]

[3 x + 2 y = 10 - x - y = - 10] : x = - 10, y = 20

x = - 10, y = 20

z = \frac{6 + 8 ai}{2 - 3 i}

z^{2} = i ∣ z ∣^{2} - 4 i

z^{1} + z^{2} = (3 - 2 i) + (4 + 3 i)

z^{2} + (2 i + 7) \cdot z + 6 + 3 i = 0

x, d i rec t r i xx + 5 = 0

What is the answer to x/(2-i)+y/(3-i)=2 ?
The answer to x/(2-i)+y/(3-i)=2 is x=-10,y=20